Optimized Regression Discontinuity Designs

2018

We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We show that this approach leads to CIs that are more efficient than conventional CIs that achieve coverage by undersmoothing or subtracting an estimate of the bias. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum mean-squared error results in CIs that are nearly efficient and that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n −2/5 , the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value.We illustrate our results in a Monte Carlo analysis and an empirical application. * We thank Don Andrews, Sebiastian Calonico, Matias Cattaneo, Max Farrell and numerous seminar and conference participants for helpful comments and suggestions. We thank Kwok Hao Lee for research assistance. All remaining errors are our own.

Section: Introductionmentioning

confidence: 99%

Simple and Honest Confidence Intervals in Nonparametric Regression

Armstrong¹,

2018

“…While restricting attention to small p (say ≤ 2) in would be severely limiting in our setting, it is not restrictive in some other problems, such as regression discontinuity. For computation of optimal weights in other settings with small p, seeHeckman (1988) andImbens and Wager (2017).…”

mentioning

confidence: 99%

Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness

Armstrong¹,

2018

We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates.Given nonparametric smoothness and/or shape restrictions on the conditional mean of the outcome variable, we derive estimators and confidence intervals (CIs) that are optimal in finite samples when the regression errors are normal with known variance.In contrast to conventional CIs, our CIs use a larger critical value that explicitly takes into account the potential bias of the estimator. When the error distribution is unknown, feasible versions of our CIs are valid asymptotically, even when √ n-inference is not possible due to lack of overlap, or low smoothness of the conditional mean. We also derive the minimum smoothness conditions on the conditional mean that are necessary for √ n-inference. When the conditional mean is restricted to be Lipschitz with a large enough bound on the Lipschitz constant, the optimal estimator reduces to a matching estimator with the number of matches set to one. We illustrate our methods in an application to the National for illuminating discussions. We also thank numerous seminar and conference participants for helpful comments and suggestions. All errors are our own.

“…Quantitative Economics 11 2020Under this condition, we only need (4) to hold for bandwidth sequences that are of the same order (nM 2 ) −1/[2(γ b −γ s )] as the optimal bandwidth h * R . 5 Note that optimal bandwidth is of the same order regardless of the performance criterion-the performance criterion only determines the optimal bandwidth constant through t * R . The next theorem collects implications of these derivations for the performance of different kernels.…”

Section: Armstrong and Kolesármentioning

confidence: 99%

Simple and Honest Confidence Intervals in Nonparametric Regression

Armstrong¹,

2018

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